sr-states.md

Grammar

S  → E $
E  → E + E₁
E  → E₁
E₁ → E₁ * E₂
E₁ → E₂
E₂ → Int

Parse table

|       |      Shift      |     Goto    | Reduce       |
| State |  +   *  Int  $  |  E   E₁  E₂ |              |
|-------|-----------------|-------------|--------------|
|   0   |          7      |  1   4   6  |              |
|   1   |  3           2  |             |              |
|   2   |                 |             | S → E$       |
|   3   |          7      |      9   6  |              |
|   4   |      5          |             | E → E₁       |
|   5   |          7      |          8  |              |
|   6   |                 |             | E₁ → E₂      |
|   7   |                 |             | E₂ → Int     |
|   8   |                 |             | E₁ → E₁ * E₂ |
|   9   |      5          |             | E → E + E₁   |

Example parse

              Stack                       Input          Action
 !  .  !  .  !  .  !  .  !  .  !    Int + Int * Int $
----------------------------------------------------------------------
 0                                  Int                  S 7
   Int 7                                +                R
 0                                   E₂                  G 6
   E₂  6                                +                R
 0                                   E₁                  G 4
   E₁  4                                +                R
 0                                   E                   G 1
   E   1                                +                S 3
          +  3                            Int            S 7
               Int 7                          *          R
             3                            E₂             G 6
               E₂  6                          *          R
             3                            E₁             G 9
               E₁  9                          *          S 5
                     *  5                       Int      S 7
                          Int 7                     $    R
                        5                       E₂       G 8
                          E₂  8                     $    R
             3                                  E₁       G 9
             3 E₁ 9                                 $    R
 0                                              E        G 1
 0  E  1                                            $    S 2
          $  2                                           R, accept